an orthotropic continuum model for the analysis of masonry structures

34 1995 TNO-95-NM-R0712(σ peak ) c = f mf tσ t , (72)Horizontal force F [kN]where the compressive yield value is made dependent of the current tensile yield value. This formulationleads to additional terms in the derivations of the numerical algorithm given in the previoussections but details about the coupled formulation will not be given here. By making use of Sections2. to 4., it is relatively straightforward to obtain the new algorithm. The results obtained withthe coupled model are given in Fig. 34 and Fig. 35. A much better agreement is found between thenew results and the experimental values. Fig. 34a shows that the collapse load is well predicted bythe model (note that the Þrst peak in the load-displacement diagram is obtained when the top andbottom horizontal bending cracks occur) and Fig. 35a shows that the expected two independentstruts can be reproduced. Therefore, for this particular structure, with a good estimate of the widthof the inactive shear band, it seems possible to reproduce the experimental results, at least to someextent. In fact, the coupled model introduces an internal length that is related to the element sizebecause the release of compressive fracture energy is coupled with tensile softening. This leads to aresponse totally inobjective with regard to the mesh size, see Fig. 34b and Fig. 35b. Upon meshreÞnement the solution in terms of load-displacement diagram converges to the uncoupled modeland, simultaneously, the width of the inactive shear band tends to zero.75.050.025.0ExperimentalIsotropic model - 8x8 elements0.00.0 1.0 2.0 3.0 4.0 5.0Horizontal displacement d [mm]Horizontal force F [kN]75.050.025.030 x 30 elements15 x 15 elements8 x 8 elementsExperimentalCoupled modelUncoupled model0.00.0 1.0 2.0 3.0 4.0 5.0Horizontal displacement d [mm]a) Vs. experimental results b) Mesh dependency of the solutionFig. 34 - Load-displacement diagram for Vermeltfoort shear wall (isotropic model)a) 8 × 8 elements b) 30 × 30 elementsFig. 35 - Principal stresses at peak for isotropic model